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Isobel Falconer

Publications and source records attributed to Isobel Falconer.

10 recordsLinked to original sources
arXiv2025

MacLaurin and Morality

Scottish mathematician Colin MacLaurin (1698-1746) is best known for his A Treatise of Fluxions (1742), An Account of Sir Isaac Newton's Philosophical Discoveries (1748), and the appellation for a type of power series. However, it is hardly known that in 1714 at the age of sixteen MacLaurin penned a short manuscript wherein he tried to apply Newtonian principles to morality, in an approach to mathematization that suggests strong continuities with earlier centuries. De viribus mentium bonipetis (On the good-seeking forces of minds) remained unpublished and hidden in the papers of the Colin Campbell Collection at the University of Edinburgh for over 250 years; it was only uncovered at the end of the twentieth century. De viribus provides a remarkable glimpse into how the young MacLaurin dealt with early Newtonianism, the tenets of the Church of Scotland, and the nascent interface between science and religion just prior to the dawn of the Scottish Enlightenment. Perhaps the most intriguing aspect of De viribus is the personal snippets related to Scottish Presbyterian morality that MacLaurin interjects throughout his mathematical discussion. These are often vague and oblique, and one must look to his mathematics, his contemporaries, and the social fabric of his surroundings to understand them. In the process, one gains insight not only into MacLaurin's family background and personal religious thought, but also into the culture and nature of teaching in Scottish universities at the time. De Viribus not only demonstrates that ideas of mathematising morality were being canvassed in Scotland much earlier than the better known, but less sophisticated, later attempts by the likes of Frances Hutcheson, David Hume and George Turnbull, but suggests continuities with approaches to mathematization in earlier centuries, providing a strong bridge into the Enlightenment era.

physics.hist-ph↗
arXiv2023

Electromagnetism in the Encyclopaedias

The paper is based on a talk given to celebrate Ørsted's discovery of electromagnetism in 1820. It gives a brief account of Ørsted's life and work, before using the evidence of articles on electricity and magnetism in the Encyclopaedia Britannica to assess understanding of the connection between the two phenomena in the 20 years before Ørsted's discovery, and the immediate reception of it.

physics.hist-ph↗
arXiv2023

Amy Ogle

A short account of the life of Amy Ogle, who, in 1876, was the first woman to come top of the Natural Sciences Tripos at Cambridge.

physics.hist-ph↗
arXiv2023

Urania Propitia

A brief account of Maria Cunitz's book Urania Propitia, commemorating the bequest of a rare copy to the London Mathematical Society by Dr A.E.L. Davis in 2020.

math.HO↗
arXiv2023

Women's participation in mathematics in Scotland, 1730-1850

The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all disciplines. However, studies of women's experiences are relatively sparse. This paper partially corrects this oversight by drawing together evidence for women's participation in mathematics in Scotland between 1730 and 1850. In considering women across all social classes, it argues for a broad definition of 'mathematics' that includes arithmetic and astronomy, and assesses women's opportunities for engagement under three headings: education, family, and sociability. It concludes that certain elements of Scottish Enlightenment culture promoted wider participation by women in mathematical activities than has previously been recognized, but that such participation continued to be circumscribed by societal views of the role of women within family formation.

math.HO↗
arXiv2019

Vortices and atoms in the Maxwellian era

The mathematical study of vortices began with Herman von Helmholtz's pioneering study in 1858. It was pursued vigorously over the next two decades, largely by British physicists and mathematicians, in two contexts: Maxwell's vortex analogy for the electromagnetic field and William Thomson's (Lord Kelvin) theory that atoms were vortex rings in an all-pervading ether. By the time of Maxwell's death in 1879, the basic laws of vortices in a perfect fluid in three-dimensional Euclidean space had been established, as had their importance to physics. Early vortex studies were embedded in a web of issues spanning the fields we now know as "mathematics" and "physics" - fields which had not yet become institutionally distinct disciplines but overlapped. This paper investigates the conceptual issues with ideas of force, matter, and space, that underlay mechanics and led to vortex models being an attractive proposition for British physicists, and how these issues played out in the mathematics of vortices, paying particular attention to problems around continuity. It concludes that while they made valuable contributions to hydrodynamics and the nascent field of topology, the British ultimately failed in their more physical objectives.

math.HO↗
arXiv2018

Phases of physics in J.D. Forbes' Dissertation Sixth for the Encyclopaedia Britannica (1856)

This paper takes James David Forbes' Encyclopaedia Britannica entry, Dissertation Sixth, as a lens to examine physics as a cognitive, practical, and social, enterprise. Forbes wrote this survey of eighteenth- and nineteenth-century mathematical and physical sciences, in 1852-6, when British "physics" was at a pivotal point in its history, situated between a discipline identified by its mathematical methods - originating in France - and one identified by its university laboratory institutions. Contemporary encyclopaedias provided a nexus for publishers, the book trade, readers, and men of science, in the formation of physics as a field. Forbes was both a witness, whose account of the progress of physics or natural philosophy can be explored at face value, and an agent, who exploited the opportunity offered by the Encyclopaedia Britannica in the mid nineteenth-century to enrol the broadly educated public, and scientific collective, illuminating the connection between the definition of physics and its forms of social practice. Forbes used the terms "physics" and "natural philosophy" interchangeably. He portrayed the field as progressed by the natural genius of great men, who curated the discipline within an associational culture that engendered true intellectual spirit. Although this societal mechanism was becoming ineffective, Forbes did not see university institutions as the way forward. Instead, running counter to his friend William Whewell, he advocated inclusion of the mechanical arts (engineering), and a strictly limited role for mathematics. He revealed tensions when the widely accepted discovery-based historiography conflicted with intellectual and moral worth, reflecting a nineteenth-century concern with spirit that cuts across twentieth-century questions about discipline and field.

physics.hist-ph↗
arXiv2017

No actual measurement ... was required: Maxwell and Cavendish's null method for the inverse square law of electrostatics

In 1877 James Clerk Maxwell and his student Donald MacAlister refined Henry Cavendish's 1773 null experiment demonstrating the absence of electricity inside a charged conductor. This null result was a mathematical prediction of the inverse square law of electrostatics, and both Cavendish and Maxwell took the experiment as verifying the law. However, Maxwell had already expressed absolute conviction in the law, based on results of Michael Faraday's. So, what was the value to him of repeating Cavendish's experiment? After assessing whether the law was as secure as he claimed, this paper explores its central importance to the electrical programme that Maxwell was pursuing. It traces the historical and conceptual re-orderings through which Maxwell established the law by constructing a tradition of null tests and asserting the superior accuracy of the method. Maxwell drew on his developing 'doctrine of method' to identify Cavendish's experiment as a member of a wider class of null methods. By doing so, he appealed to the null practices of telegraph engineers, diverted attention from the flawed logic of the method, and sought to localise issues around the mapping of numbers onto instrumental indications, on the grounds that 'no actual measurement ... was required'.

physics.hist-ph↗
arXiv2015

Editing Cavendish: Maxwell and The Electrical Researches of Henry Cavendish

During the last five years of his life, 1874-79, James Clerk Maxwell was absorbed in editing the electrical researches of Henry Cavendish, performed 100 years earlier. This endeavour is often assumed to be a work of duty to the Cavendish family, and an unfortunate waste of Maxwell's time. By looking at the history of Cavendish's papers, and the editorial choices that Maxwell made, this paper questions this assumption, considering the importance of Cavendish's experiments in Maxwell's electrical programme, and the implications that he may have derived for developing a doctrine of experimental method.

physics.hist-ph↗